SINGLE 2-LEVEL ION IN AN ANHARMONIC-OSCILLATOR TRAP - TIME EVOLUTION OF THE Q-FUNCTION AND POPULATION-INVERSION

We investigate the time evolution of the population inversion as well as the Q function for center-of-mass motion for a two-level ion, inter acting with single-mode laser light field, in an anharmonic-oscillator trap. The anharmonicities of the trap are quantified in terms of the deformation parameter of the q-analog trap. For tau=0.003 (q=e(tau)) t he collapses and revivals of population inversion become well-defined facilitating experimental observation, but for large tau similar to 0. 1 the time dependence of population inversion is completely wiped out. The quasiprobability function shows an atypical behavior with a singl e peak at t=0 splitting up into as many as seven fragments (at t=130) during collapse and at a later time these segments come together to si gnal the revival of population inversion. A small degree of anharmonic ity is Seen to enhance the coherence of the ion-trap system, whereas f or large tau (similar to 0.1 in the present context) the coherence is completely lost.